Contest Duration: - (local time) (100 minutes) Back to Home
B - Crane and Turtle /

Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 1 \leq X \leq 100
• 1 \leq Y \leq 100
• 入力中のすべての値は整数である。

入力

X Y


入力例 1

3 8


出力例 1

Yes


「庭にいる動物の総数は 3 匹で、それらの動物の足の総数は 8 本である」という発言は、鶴が 2 羽、亀が 1 匹いる場合に正しいため、発言が正しいような鶴と亀の数の組合せは存在します。

入力例 2

2 100


出力例 2

No


この発言が正しいような鶴と亀の数の組合せは存在しません。

入力例 3

1 2


出力例 3

Yes


Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

• 1 \leq X \leq 100
• 1 \leq Y \leq 100
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y


Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8


Sample Output 1

Yes


The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100


Sample Output 2

No


There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2


Sample Output 3

Yes


We also consider the case in which there are only cranes or only turtles.